The Barcelona striker was banned from all football-related activity for biting Italy’s Giorgio Chiellini during Uruguay’s 1-0 World Cup win on June 24.
The Court of Arbitration for Sport (CAS) has agreed to deal with his appeal as an ‘express hearing’ so that a decision is reached before the start of the Spanish season.
Barcelona are also asking CAS to allow Suarez to train with his team-mates for the duration of any ban – under the FIFA ban he is not permitted even to enter a training ground.
The sanction imposed by FIFA on Suarez also includes a nine-month international ban from playing for Uruguay.
FIFA’s appeals committee rejected an appeal in mid-July but the ban did not prevent Suarez moving from Liverpool to Barcelona for £75million.
If Suarez’s four-month ban stands, he would be in line to make his debut in El Clasico against Real Madrid on the weekend of October 25.
The international players’ union FIFPro has claimed that the terms of the ban infringes Suarez’s right to work.
A statement issued in June said: "The fact that Suarez is prohibited from working for a long period must be addressed as it directly infringes his right to work. Luis Suarez deserves all the support he needs including legal support in the appeal case in order to achieve a reduction of the sanctions."
Barcelona’s fellow new signing Jeremy Mathieu believes Suarez is a strong character who will learn from his mistakes, and will show Barca fans his true qualities.
Mathieu said: "We know Luis Suarez has a very strong character and that he is a great player. I think after the ban he will show what he is capable of and that everyone will be very happy to have him at Barcelona."
Mathieu, speaking at Barcelona’s pre-season training camp at St George’s Park near Burton, was asked what he would do if Suarez bit him.
The French defender replied: "To be honest, if he bites me, I will do nothing. But I think he will learn from his mistakes for sure. He is a great player, and hopefully that will never happen again."